Moreover, it is noteworthy that the inclusion function based on mixed-monotone decomposition functions can be used alongside any existing inclusion functions, where
the “best of them"  (by virtue of an intersection property) is chosen,
since we observed that  in general, no single inclusion function consistently outperforms all others. Further more, our proposed inclusion function can be directly and simply integrated in to existing set inversion, constrained reachability and interval observer algorithms, e.g., [1]}, [2]}, [3]}, without much modifications. Finally, to demonstrate the effectiveness of the proposed algorithms for decomposition function construction and set inversion, we compare them with existing inclusion/decomposition functions in the literature.
